Skip to main content
Log in

Condensate Fraction in Liquid 4He

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

The condensate fraction n 0 in the ground state of liquid 4He is computed by means of an unbiased Quantum Monte Carlo technique. Unlike previous calculations of the same type, the method adopted here is in principle exact, errors being only statistical. At the equilibrium density, our estimate for n 0 is 0.069 ± 0.005; this is consistent with the most recent experimental measurements, but significantly lower than most existing theoretical estimates. Results are provided in the density range from the spinodal (where n 0 is maximum, ≈30%) up to the melting density. The condensate fraction remains finite in the high pressure metastable liquid, decaying exponentially with density.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. F.London, Nature 141,643 (1938).

    Google Scholar 

  2. See,for instance,D. Pines, and P. Nozières, The Theory of Quantum Liquids, Vol.II, Addison-Wesley, New York, (1992).

    Google Scholar 

  3. See,for instance,C.J.Pethick and H.Smith,Bose Einstein Condensation in Dilute Gases, (Cambridge University Press, Cambridge (2001).

    Google Scholar 

  4. A.Miller, D.Pines,and P.Nozières,Phys.Rev.127,1452 (1962).

    Google Scholar 

  5. P.C.Hohenberg and P.M.Platzman,Phys.Rev.152,198 (1966).

    Google Scholar 

  6. For a review,see,for instance,H.R.Glyde,Excitations in Liquid and Solid Helium, Oxford Science Publication, Oxford,(1995).

    Google Scholar 

  7. V.F.Sears, E.C.Svensson, P.Martel,and A.D.B.Woods,Phys.Rev.Lett.49,279 (1982).

    Google Scholar 

  8. W.M.Snow, Y.Wang and P.E.Sokol,Europhys.Lett.19,403 (1992).

    Google Scholar 

  9. P.E.Sokol in Bose-Einstein Condensation,A.Griffin, D.W.Snoke,and S.Stringari (eds.),Cambridge University Press, Cambridge (1995).

    Google Scholar 

  10. R.T.Azuah, W.G.Stirling, H.R.Glyde, M.Boninsegni, P.E.Sokol,and S.M.Ben-nington,Phys.Rev.B 56,14620 (1997).

    Google Scholar 

  11. H.R. Glyde, R.T.Azuah,and W.G.Stirling, Phys.Rev.B 62,14337 (2000).

    Google Scholar 

  12. A.F.G. Wyatt, Nature 391,56 (1998).

    Google Scholar 

  13. S.Moroni, G.Senatore, and S.Fantoni, Phys.Rev. B 55,1040 (1997) and references therein.

    Google Scholar 

  14. T. MacFarland, S.A. Vitiello, L.Reatto, G.V. Chester, and M.H.Kalos, Phys.Rev. B 50,13577 (1994)

    Google Scholar 

  15. D.M. Ceperley, and M.H.Kalos in Monte Carlo Methods in Statistical Physics, K. Binder (ed.) Springer-Verlag, Berlin (1979).

    Google Scholar 

  16. P.A. Whitlock and R.M. Panoff, Can.J.Phys.65,1409 (1987).

    Google Scholar 

  17. J.Boronat and J.Casulleras, Phys.Rev.B 49,8920 (1994)

    Google Scholar 

  18. D.M. Ceperley, Rev.Mod.Phys.67,2 (1995).

    Google Scholar 

  19. D.M. Ceperley and E.L. Pollock, Can.J.Phys.65,1416 (1987).

    Google Scholar 

  20. S.Baroni and S.Moroni, Phys.Rev.Lett.82,4745 (1999).

    Google Scholar 

  21. See,for instance, A.Sarsa, K.E. Schmidt, and W.R. Magro, J.Chem.Phys.113,1366 (2000).

    Google Scholar 

  22. Strictly speaking,ΨT is required to be non-orthogonal to the true ground state wave function.For a Bose system this is not a problem,as the ground state wave function can always be chosen real and positive,and therefore any positive-de nite function ΨT satisfies the non-orthogonality requirement.It is also necessary for ΨT to be non-negative,in order for (2)to be treated as a probability.

  23. The normalization for n (r)can be xed through the behavior of n(r)in r →0 limit.See Ref.13,for details.

  24. R.A. Aziz, V.P.S.Nain, J.S. Carley, W.L. Taylor, and G.T. McConville, J.Chem. Phys.70,4330 (1979).

    Google Scholar 

  25. S.C. Hall, and H.J. Maris, J.Low Temp.Phys.107,263 (1997).

    Google Scholar 

  26. A.R. Janzen and R.A. Aziz, J.Chem.Phys.107,914 (1997).

    Google Scholar 

  27. S.Moroni, F.Pederiva, S.Fantoni, and M.Boninsegni, Phys.Rev.Lett.84,2650 (2000).

    Google Scholar 

  28. M.Boninsegni, C.Pierleoni, and D.M. Ceperley, Phys.Rev.Lett.72,1854 (1994).

    Google Scholar 

  29. See,for instance, F.Caupin, S.Balibar, and H.J. Maris,Physica B 329-333,356 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Moroni, S., Boninsegni, M. Condensate Fraction in Liquid 4He. Journal of Low Temperature Physics 136, 129–137 (2004). https://doi.org/10.1023/B:JOLT.0000038518.10132.30

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOLT.0000038518.10132.30

Navigation